%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT330+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:23 AM UTC 2025
% Result : Theorem 4.35s 4.52s
% Output : Proof 4.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT330+1 : TPTP v9.0.0. Released v3.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 20:23:56 EDT 2025
% 0.11/0.33 % CPUTime :
% 4.35/4.52 % SZS status Theorem
% 4.35/4.52 % SZS output start Proof
% 4.35/4.52 tff(r3_lattices_type, type, (
% 4.35/4.52 r3_lattices: ( $i * $i * $i ) > $o)).
% 4.35/4.52 tff(tptp_fun_B_1_type, type, (
% 4.35/4.52 tptp_fun_B_1: $i)).
% 4.35/4.52 tff(tptp_fun_D_2_type, type, (
% 4.35/4.52 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 4.35/4.52 tff(u1_struct_0_type, type, (
% 4.35/4.52 u1_struct_0: $i > $i)).
% 4.35/4.52 tff(tptp_fun_A_0_type, type, (
% 4.35/4.52 tptp_fun_A_0: $i)).
% 4.35/4.52 tff(a_2_0_filter_2_type, type, (
% 4.35/4.52 a_2_0_filter_2: ( $i * $i ) > $i)).
% 4.35/4.52 tff(k22_filter_2_type, type, (
% 4.35/4.52 k22_filter_2: ( $i * $i * $i ) > $i)).
% 4.35/4.52 tff(k5_lattices_type, type, (
% 4.35/4.52 k5_lattices: $i > $i)).
% 4.35/4.52 tff(m1_subset_1_type, type, (
% 4.35/4.52 m1_subset_1: ( $i * $i ) > $o)).
% 4.35/4.52 tff(r2_hidden_type, type, (
% 4.35/4.52 r2_hidden: ( $i * $i ) > $o)).
% 4.35/4.52 tff(r1_filter_2_type, type, (
% 4.35/4.52 r1_filter_2: ( $i * $i * $i ) > $o)).
% 4.35/4.52 tff(k1_zfmisc_1_type, type, (
% 4.35/4.52 k1_zfmisc_1: $i > $i)).
% 4.35/4.52 tff(m2_lattice4_type, type, (
% 4.35/4.52 m2_lattice4: ( $i * $i ) > $o)).
% 4.35/4.52 tff(k18_filter_2_type, type, (
% 4.35/4.52 k18_filter_2: ( $i * $i ) > $i)).
% 4.35/4.52 tff(v10_lattices_type, type, (
% 4.35/4.52 v10_lattices: $i > $o)).
% 4.35/4.52 tff(l3_lattices_type, type, (
% 4.35/4.52 l3_lattices: $i > $o)).
% 4.35/4.52 tff(v3_struct_0_type, type, (
% 4.35/4.52 v3_struct_0: $i > $o)).
% 4.35/4.52 tff(v13_lattices_type, type, (
% 4.35/4.52 v13_lattices: $i > $o)).
% 4.35/4.52 tff(v1_xboole_0_type, type, (
% 4.35/4.52 v1_xboole_0: $i > $o)).
% 4.35/4.52 tff(m2_filter_2_type, type, (
% 4.35/4.52 m2_filter_2: ( $i * $i ) > $o)).
% 4.35/4.52 tff(l1_struct_0_type, type, (
% 4.35/4.52 l1_struct_0: $i > $o)).
% 4.35/4.52 tff(l2_lattices_type, type, (
% 4.35/4.52 l2_lattices: $i > $o)).
% 4.35/4.52 tff(l1_lattices_type, type, (
% 4.35/4.52 l1_lattices: $i > $o)).
% 4.35/4.52 tff(1,assumption,(r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))), introduced(assumption)).
% 4.35/4.52 tff(2,plain,
% 4.35/4.52 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))),
% 4.35/4.52 inference(bind,[status(th)],[])).
% 4.35/4.52 tff(3,plain,
% 4.35/4.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 4.35/4.52 inference(quant_intro,[status(thm)],[2])).
% 4.35/4.52 tff(4,plain,
% 4.35/4.52 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))))),
% 4.35/4.52 inference(bind,[status(th)],[])).
% 4.35/4.52 tff(5,plain,
% 4.35/4.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 4.35/4.52 inference(quant_intro,[status(thm)],[4])).
% 4.35/4.52 tff(6,plain,
% 4.35/4.52 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))))),
% 4.35/4.52 inference(bind,[status(th)],[])).
% 4.35/4.52 tff(7,plain,
% 4.35/4.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 4.35/4.52 inference(quant_intro,[status(thm)],[6])).
% 4.35/4.52 tff(8,plain,
% 4.35/4.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 4.35/4.52 inference(transitivity,[status(thm)],[7, 5])).
% 4.35/4.52 tff(9,plain,
% 4.35/4.52 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))))),
% 4.35/4.52 inference(bind,[status(th)],[])).
% 4.35/4.52 tff(10,plain,
% 4.35/4.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 4.35/4.52 inference(quant_intro,[status(thm)],[9])).
% 4.35/4.52 tff(11,plain,
% 4.35/4.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 4.35/4.52 inference(rewrite,[status(thm)],[])).
% 4.35/4.52 tff(12,plain,
% 4.35/4.52 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))))),
% 4.35/4.52 inference(bind,[status(th)],[])).
% 4.35/4.52 tff(13,plain,
% 4.35/4.52 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 4.35/4.52 inference(quant_intro,[status(thm)],[12])).
% 4.35/4.52 tff(14,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_filter_2')).
% 4.35/4.52 tff(15,plain,
% 4.35/4.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 4.35/4.52 inference(modus_ponens,[status(thm)],[14, 13])).
% 4.35/4.52 tff(16,plain,
% 4.35/4.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 4.35/4.52 inference(modus_ponens,[status(thm)],[15, 11])).
% 4.35/4.52 tff(17,plain,(
% 4.35/4.52 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 4.35/4.52 inference(skolemize,[status(sab)],[16])).
% 4.35/4.52 tff(18,plain,
% 4.35/4.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 4.35/4.52 inference(modus_ponens,[status(thm)],[17, 10])).
% 4.35/4.52 tff(19,plain,
% 4.35/4.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 4.35/4.52 inference(modus_ponens,[status(thm)],[18, 8])).
% 4.35/4.52 tff(20,plain,
% 4.35/4.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 4.35/4.52 inference(modus_ponens,[status(thm)],[19, 3])).
% 4.35/4.52 tff(21,plain,
% 4.35/4.52 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 4.35/4.52 inference(rewrite,[status(thm)],[])).
% 4.35/4.52 tff(22,plain,
% 4.35/4.52 ((~(r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~v13_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))),
% 4.35/4.52 inference(rewrite,[status(thm)],[])).
% 4.35/4.52 tff(23,plain,
% 4.35/4.52 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~v13_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 4.35/4.52 inference(monotonicity,[status(thm)],[22])).
% 4.35/4.52 tff(24,plain,
% 4.35/4.52 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~v13_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 4.35/4.52 inference(transitivity,[status(thm)],[23, 21])).
% 4.35/4.52 tff(25,plain,
% 4.35/4.52 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 4.35/4.52 inference(rewrite,[status(thm)],[])).
% 4.35/4.52 tff(26,plain,
% 4.35/4.52 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (v13_lattices(A) => r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 4.35/4.52 inference(rewrite,[status(thm)],[])).
% 4.35/4.52 tff(27,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (v13_lattices(A) => r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t67_filter_2')).
% 4.35/4.52 tff(28,plain,
% 4.35/4.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 4.35/4.52 inference(modus_ponens,[status(thm)],[27, 26])).
% 4.35/4.52 tff(29,plain,
% 4.35/4.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 4.35/4.52 inference(modus_ponens,[status(thm)],[28, 25])).
% 4.35/4.52 tff(30,plain,
% 4.35/4.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 4.35/4.52 inference(modus_ponens,[status(thm)],[29, 25])).
% 4.35/4.52 tff(31,plain,
% 4.35/4.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 4.35/4.52 inference(modus_ponens,[status(thm)],[30, 25])).
% 4.35/4.52 tff(32,plain,
% 4.35/4.52 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))),
% 4.35/4.52 inference(modus_ponens,[status(thm)],[31, 24])).
% 4.35/4.52 tff(33,plain,
% 4.35/4.52 (l3_lattices(A!0)),
% 4.35/4.52 inference(and_elim,[status(thm)],[32])).
% 4.35/4.52 tff(34,plain,
% 4.35/4.52 (v10_lattices(A!0)),
% 4.35/4.52 inference(and_elim,[status(thm)],[32])).
% 4.35/4.52 tff(35,plain,
% 4.35/4.52 (~v3_struct_0(A!0)),
% 4.35/4.52 inference(and_elim,[status(thm)],[32])).
% 4.35/4.52 tff(36,plain,
% 4.35/4.52 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))),
% 4.35/4.52 inference(rewrite,[status(thm)],[])).
% 4.35/4.52 tff(37,plain,
% 4.35/4.52 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))),
% 4.37/4.52 inference(quant_inst,[status(thm)],[])).
% 4.37/4.52 tff(38,plain,
% 4.37/4.52 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))),
% 4.37/4.52 inference(modus_ponens,[status(thm)],[37, 36])).
% 4.37/4.52 tff(39,plain,
% 4.37/4.52 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))),
% 4.37/4.52 inference(unit_resolution,[status(thm)],[38, 35, 34, 33, 20])).
% 4.37/4.52 tff(40,plain,
% 4.37/4.52 (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 4.37/4.52 inference(and_elim,[status(thm)],[32])).
% 4.37/4.52 tff(41,plain,
% 4.37/4.52 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 4.37/4.52 inference(or_elim,[status(thm)],[40])).
% 4.37/4.52 tff(42,plain,
% 4.37/4.52 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))),
% 4.37/4.52 inference(rewrite,[status(thm)],[])).
% 4.37/4.52 tff(43,plain,
% 4.37/4.52 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))),
% 4.37/4.52 inference(quant_inst,[status(thm)],[])).
% 4.37/4.52 tff(44,plain,
% 4.37/4.52 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1))),
% 4.37/4.52 inference(modus_ponens,[status(thm)],[43, 42])).
% 4.37/4.52 tff(45,plain,
% 4.37/4.52 (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)),
% 4.37/4.52 inference(unit_resolution,[status(thm)],[44, 41, 39])).
% 4.37/4.52 tff(46,plain,
% 4.37/4.52 (a_2_0_filter_2(A!0, B!1) = k18_filter_2(A!0, B!1)),
% 4.37/4.52 inference(symmetry,[status(thm)],[45])).
% 4.37/4.52 tff(47,plain,
% 4.37/4.52 (m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0) <=> m2_lattice4(k18_filter_2(A!0, B!1), A!0)),
% 4.37/4.52 inference(monotonicity,[status(thm)],[46])).
% 4.37/4.52 tff(48,plain,
% 4.37/4.52 (m2_lattice4(k18_filter_2(A!0, B!1), A!0) <=> m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)),
% 4.37/4.52 inference(symmetry,[status(thm)],[47])).
% 4.37/4.52 tff(49,plain,
% 4.37/4.52 (^[A: $i, B: $i] : refl((m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 4.37/4.52 inference(bind,[status(th)],[])).
% 4.37/4.52 tff(50,plain,
% 4.37/4.52 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 4.37/4.52 inference(quant_intro,[status(thm)],[49])).
% 4.37/4.52 tff(51,plain,
% 4.37/4.52 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k18_filter_2(A, B), A)))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k18_filter_2(A, B), A)) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(52,plain,
% 4.37/4.53 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[51])).
% 4.37/4.53 tff(53,plain,
% 4.37/4.53 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(54,plain,
% 4.37/4.53 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(55,plain,
% 4.37/4.53 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[54])).
% 4.37/4.53 tff(56,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k18_filter_2')).
% 4.37/4.53 tff(57,plain,
% 4.37/4.53 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[56, 55])).
% 4.37/4.53 tff(58,plain,
% 4.37/4.53 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[57, 53])).
% 4.37/4.53 tff(59,plain,(
% 4.37/4.53 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 4.37/4.53 inference(skolemize,[status(sab)],[58])).
% 4.37/4.53 tff(60,plain,
% 4.37/4.53 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[59, 52])).
% 4.37/4.53 tff(61,plain,
% 4.37/4.53 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[60, 50])).
% 4.37/4.53 tff(62,plain,
% 4.37/4.53 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(63,plain,
% 4.37/4.53 ((m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(64,plain,
% 4.37/4.53 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0)))),
% 4.37/4.53 inference(monotonicity,[status(thm)],[63])).
% 4.37/4.53 tff(65,plain,
% 4.37/4.53 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))),
% 4.37/4.53 inference(transitivity,[status(thm)],[64, 62])).
% 4.37/4.53 tff(66,plain,
% 4.37/4.53 ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 4.37/4.53 inference(quant_inst,[status(thm)],[])).
% 4.37/4.53 tff(67,plain,
% 4.37/4.53 ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0)),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[66, 65])).
% 4.37/4.53 tff(68,plain,
% 4.37/4.53 (m2_filter_2(k18_filter_2(A!0, B!1), A!0)),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[67, 35, 34, 33, 41, 61])).
% 4.37/4.53 tff(69,plain,
% 4.37/4.53 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(70,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[69])).
% 4.37/4.53 tff(71,plain,
% 4.37/4.53 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(72,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[71])).
% 4.37/4.53 tff(73,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 4.37/4.53 inference(transitivity,[status(thm)],[72, 70])).
% 4.37/4.53 tff(74,plain,
% 4.37/4.53 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(75,plain,
% 4.37/4.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[74])).
% 4.37/4.53 tff(76,plain,
% 4.37/4.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(77,plain,
% 4.37/4.53 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(78,plain,
% 4.37/4.53 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[77])).
% 4.37/4.53 tff(79,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 4.37/4.53 tff(80,plain,
% 4.37/4.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[79, 78])).
% 4.37/4.53 tff(81,plain,
% 4.37/4.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[80, 76])).
% 4.37/4.53 tff(82,plain,(
% 4.37/4.53 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 4.37/4.53 inference(skolemize,[status(sab)],[81])).
% 4.37/4.53 tff(83,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[82, 75])).
% 4.37/4.53 tff(84,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[83, 73])).
% 4.37/4.53 tff(85,plain,
% 4.37/4.53 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(86,plain,
% 4.37/4.53 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 4.37/4.53 inference(quant_inst,[status(thm)],[])).
% 4.37/4.53 tff(87,plain,
% 4.37/4.53 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[86, 85])).
% 4.37/4.53 tff(88,plain,
% 4.37/4.53 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[87, 35, 34, 33, 84])).
% 4.37/4.53 tff(89,plain,
% 4.37/4.53 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(90,plain,
% 4.37/4.53 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))))),
% 4.37/4.53 inference(quant_inst,[status(thm)],[])).
% 4.37/4.53 tff(91,plain,
% 4.37/4.53 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[90, 89])).
% 4.37/4.53 tff(92,plain,
% 4.37/4.53 (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[91, 88, 68])).
% 4.37/4.53 tff(93,plain,
% 4.37/4.53 ((v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0))) | m2_lattice4(k18_filter_2(A!0, B!1), A!0)),
% 4.37/4.53 inference(tautology,[status(thm)],[])).
% 4.37/4.53 tff(94,plain,
% 4.37/4.53 (m2_lattice4(k18_filter_2(A!0, B!1), A!0)),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[93, 92])).
% 4.37/4.53 tff(95,plain,
% 4.37/4.53 (m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[94, 48])).
% 4.37/4.53 tff(96,plain,
% 4.37/4.53 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(97,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[96])).
% 4.37/4.53 tff(98,plain,
% 4.37/4.53 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(99,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[98])).
% 4.37/4.53 tff(100,plain,
% 4.37/4.53 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(101,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[100])).
% 4.37/4.53 tff(102,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 4.37/4.53 inference(transitivity,[status(thm)],[101, 99])).
% 4.37/4.53 tff(103,plain,
% 4.37/4.53 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(104,plain,
% 4.37/4.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[103])).
% 4.37/4.53 tff(105,plain,
% 4.37/4.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(106,plain,
% 4.37/4.53 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(107,plain,
% 4.37/4.53 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[106])).
% 4.37/4.53 tff(108,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 4.37/4.53 tff(109,plain,
% 4.37/4.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[108, 107])).
% 4.37/4.53 tff(110,plain,
% 4.37/4.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[109, 105])).
% 4.37/4.53 tff(111,plain,(
% 4.37/4.53 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 4.37/4.53 inference(skolemize,[status(sab)],[110])).
% 4.37/4.53 tff(112,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[111, 104])).
% 4.37/4.53 tff(113,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[112, 102])).
% 4.37/4.53 tff(114,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[113, 97])).
% 4.37/4.53 tff(115,plain,
% 4.37/4.53 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(116,plain,
% 4.37/4.53 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 4.37/4.53 inference(quant_inst,[status(thm)],[])).
% 4.37/4.53 tff(117,plain,
% 4.37/4.53 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[116, 115])).
% 4.37/4.53 tff(118,plain,
% 4.37/4.53 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[117, 35, 34, 33, 114])).
% 4.37/4.53 tff(119,plain,
% 4.37/4.53 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(120,plain,
% 4.37/4.53 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 4.37/4.53 inference(quant_inst,[status(thm)],[])).
% 4.37/4.53 tff(121,plain,
% 4.37/4.53 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[120, 119])).
% 4.37/4.53 tff(122,plain,
% 4.37/4.53 ((~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[121, 118])).
% 4.37/4.53 tff(123,plain,
% 4.37/4.53 (m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[122, 95])).
% 4.37/4.53 tff(124,plain,
% 4.37/4.53 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(125,plain,
% 4.37/4.53 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[124])).
% 4.37/4.53 tff(126,plain,
% 4.37/4.53 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(127,plain,
% 4.37/4.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[126])).
% 4.37/4.53 tff(128,plain,
% 4.37/4.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(129,plain,
% 4.37/4.53 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(130,plain,
% 4.37/4.53 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[129])).
% 4.37/4.53 tff(131,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 4.37/4.53 tff(132,plain,
% 4.37/4.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[131, 130])).
% 4.37/4.53 tff(133,plain,
% 4.37/4.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[132, 128])).
% 4.37/4.53 tff(134,plain,(
% 4.37/4.53 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 4.37/4.53 inference(skolemize,[status(sab)],[133])).
% 4.37/4.53 tff(135,plain,
% 4.37/4.53 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[134, 127])).
% 4.37/4.53 tff(136,plain,
% 4.37/4.53 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[135, 125])).
% 4.37/4.53 tff(137,plain,
% 4.37/4.53 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(138,plain,
% 4.37/4.53 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 4.37/4.53 inference(quant_inst,[status(thm)],[])).
% 4.37/4.53 tff(139,plain,
% 4.37/4.53 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[138, 137])).
% 4.37/4.53 tff(140,plain,
% 4.37/4.53 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[139, 33, 136])).
% 4.37/4.53 tff(141,plain,
% 4.37/4.53 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 4.37/4.53 inference(tautology,[status(thm)],[])).
% 4.37/4.53 tff(142,plain,
% 4.37/4.53 (l2_lattices(A!0)),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[141, 140])).
% 4.37/4.53 tff(143,plain,
% 4.37/4.53 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(144,plain,
% 4.37/4.53 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[143])).
% 4.37/4.53 tff(145,plain,
% 4.37/4.53 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(146,plain,
% 4.37/4.53 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(147,plain,
% 4.37/4.53 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[146])).
% 4.37/4.53 tff(148,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 4.37/4.53 tff(149,plain,
% 4.37/4.53 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[148, 147])).
% 4.37/4.53 tff(150,plain,
% 4.37/4.53 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[149, 145])).
% 4.37/4.53 tff(151,plain,(
% 4.37/4.53 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 4.37/4.53 inference(skolemize,[status(sab)],[150])).
% 4.37/4.53 tff(152,plain,
% 4.37/4.53 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[151, 144])).
% 4.37/4.53 tff(153,plain,
% 4.37/4.53 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(154,plain,
% 4.37/4.53 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 4.37/4.53 inference(quant_inst,[status(thm)],[])).
% 4.37/4.53 tff(155,plain,
% 4.37/4.53 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[154, 153])).
% 4.37/4.53 tff(156,plain,
% 4.37/4.53 (l1_struct_0(A!0)),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[155, 152, 142])).
% 4.37/4.53 tff(157,plain,
% 4.37/4.53 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(158,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[157])).
% 4.37/4.53 tff(159,plain,
% 4.37/4.53 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(160,plain,
% 4.37/4.53 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[159])).
% 4.37/4.53 tff(161,plain,
% 4.37/4.53 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(162,plain,
% 4.37/4.53 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(163,plain,
% 4.37/4.53 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[162])).
% 4.37/4.53 tff(164,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 4.37/4.53 tff(165,plain,
% 4.37/4.53 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[164, 163])).
% 4.37/4.53 tff(166,plain,
% 4.37/4.53 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[165, 161])).
% 4.37/4.53 tff(167,plain,(
% 4.37/4.53 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 4.37/4.53 inference(skolemize,[status(sab)],[166])).
% 4.37/4.53 tff(168,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[167, 160])).
% 4.37/4.53 tff(169,plain,
% 4.37/4.53 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[168, 158])).
% 4.37/4.53 tff(170,plain,
% 4.37/4.53 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(171,plain,
% 4.37/4.53 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(172,plain,
% 4.37/4.53 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 4.37/4.53 inference(monotonicity,[status(thm)],[171])).
% 4.37/4.53 tff(173,plain,
% 4.37/4.53 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 4.37/4.53 inference(transitivity,[status(thm)],[172, 170])).
% 4.37/4.53 tff(174,plain,
% 4.37/4.53 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 4.37/4.53 inference(quant_inst,[status(thm)],[])).
% 4.37/4.53 tff(175,plain,
% 4.37/4.53 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 4.37/4.53 inference(modus_ponens,[status(thm)],[174, 173])).
% 4.37/4.53 tff(176,plain,
% 4.37/4.53 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[175, 35, 169])).
% 4.37/4.53 tff(177,plain,
% 4.37/4.53 (~v1_xboole_0(u1_struct_0(A!0))),
% 4.37/4.53 inference(unit_resolution,[status(thm)],[176, 156])).
% 4.37/4.53 tff(178,plain,
% 4.37/4.53 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(179,plain,
% 4.37/4.53 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[178])).
% 4.37/4.53 tff(180,plain,
% 4.37/4.53 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(181,plain,
% 4.37/4.53 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[180])).
% 4.37/4.53 tff(182,plain,
% 4.37/4.53 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 4.37/4.53 inference(transitivity,[status(thm)],[181, 179])).
% 4.37/4.53 tff(183,plain,
% 4.37/4.53 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 4.37/4.53 inference(bind,[status(th)],[])).
% 4.37/4.53 tff(184,plain,
% 4.37/4.53 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 4.37/4.53 inference(quant_intro,[status(thm)],[183])).
% 4.37/4.53 tff(185,plain,
% 4.37/4.53 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 4.37/4.53 inference(rewrite,[status(thm)],[])).
% 4.37/4.53 tff(186,plain,
% 4.37/4.53 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))) <=> (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ((~v1_xboole_0(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))))),
% 4.37/4.54 inference(bind,[status(th)],[])).
% 4.37/4.54 tff(187,plain,
% 4.37/4.54 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 4.37/4.54 inference(quant_intro,[status(thm)],[186])).
% 4.37/4.54 tff(188,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_filter_2')).
% 4.37/4.54 tff(189,plain,
% 4.37/4.54 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[188, 187])).
% 4.37/4.54 tff(190,plain,
% 4.37/4.54 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[189, 185])).
% 4.37/4.54 tff(191,plain,(
% 4.37/4.54 ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))),
% 4.37/4.54 inference(skolemize,[status(sab)],[190])).
% 4.37/4.54 tff(192,plain,
% 4.37/4.54 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[191, 184])).
% 4.37/4.54 tff(193,plain,
% 4.37/4.54 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[192, 182])).
% 4.37/4.54 tff(194,plain,
% 4.37/4.54 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))),
% 4.37/4.54 inference(rewrite,[status(thm)],[])).
% 4.37/4.54 tff(195,plain,
% 4.37/4.54 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))),
% 4.37/4.54 inference(quant_inst,[status(thm)],[])).
% 4.37/4.54 tff(196,plain,
% 4.37/4.54 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[195, 194])).
% 4.37/4.54 tff(197,plain,
% 4.37/4.54 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))),
% 4.37/4.54 inference(unit_resolution,[status(thm)],[196, 193, 177])).
% 4.37/4.54 tff(198,plain,
% 4.37/4.54 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | ((~m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | (~m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C))))))))))),
% 4.37/4.54 inference(rewrite,[status(thm)],[])).
% 4.37/4.54 tff(199,plain,
% 4.37/4.54 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | ((~m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C))))))))))),
% 4.37/4.54 inference(quant_inst,[status(thm)],[])).
% 4.37/4.54 tff(200,plain,
% 4.37/4.54 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | (~m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C)))))))))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[199, 198])).
% 4.37/4.54 tff(201,plain,
% 4.37/4.54 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C)))))))))),
% 4.37/4.54 inference(unit_resolution,[status(thm)],[200, 197, 123])).
% 4.37/4.54 tff(202,plain,
% 4.37/4.54 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 4.37/4.54 inference(tautology,[status(thm)],[])).
% 4.37/4.54 tff(203,plain,
% 4.37/4.54 (l1_lattices(A!0)),
% 4.37/4.54 inference(unit_resolution,[status(thm)],[202, 140])).
% 4.37/4.54 tff(204,plain,
% 4.37/4.54 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))))),
% 4.37/4.54 inference(bind,[status(th)],[])).
% 4.37/4.54 tff(205,plain,
% 4.37/4.54 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 4.37/4.54 inference(quant_intro,[status(thm)],[204])).
% 4.37/4.54 tff(206,plain,
% 4.37/4.54 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))))),
% 4.37/4.54 inference(bind,[status(th)],[])).
% 4.37/4.54 tff(207,plain,
% 4.37/4.54 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 4.37/4.54 inference(quant_intro,[status(thm)],[206])).
% 4.37/4.54 tff(208,plain,
% 4.37/4.54 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 4.37/4.54 inference(rewrite,[status(thm)],[])).
% 4.37/4.54 tff(209,plain,
% 4.37/4.54 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))))),
% 4.37/4.54 inference(bind,[status(th)],[])).
% 4.37/4.54 tff(210,plain,
% 4.37/4.54 (![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 4.37/4.54 inference(quant_intro,[status(thm)],[209])).
% 4.37/4.54 tff(211,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_lattices')).
% 4.37/4.54 tff(212,plain,
% 4.37/4.54 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[211, 210])).
% 4.37/4.54 tff(213,plain,
% 4.37/4.54 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[212, 208])).
% 4.37/4.54 tff(214,plain,(
% 4.37/4.54 ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 4.37/4.54 inference(skolemize,[status(sab)],[213])).
% 4.37/4.54 tff(215,plain,
% 4.37/4.54 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[214, 207])).
% 4.37/4.54 tff(216,plain,
% 4.37/4.54 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[215, 205])).
% 4.37/4.54 tff(217,plain,
% 4.37/4.54 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))),
% 4.37/4.54 inference(rewrite,[status(thm)],[])).
% 4.37/4.54 tff(218,plain,
% 4.37/4.54 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))),
% 4.37/4.54 inference(quant_inst,[status(thm)],[])).
% 4.37/4.54 tff(219,plain,
% 4.37/4.54 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[218, 217])).
% 4.37/4.54 tff(220,plain,
% 4.37/4.54 (m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0))),
% 4.37/4.54 inference(unit_resolution,[status(thm)],[219, 35, 216])).
% 4.37/4.54 tff(221,plain,
% 4.37/4.54 (m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))),
% 4.37/4.54 inference(unit_resolution,[status(thm)],[220, 203])).
% 4.37/4.54 tff(222,plain,
% 4.37/4.54 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))))),
% 4.37/4.54 inference(bind,[status(th)],[])).
% 4.37/4.54 tff(223,plain,
% 4.37/4.54 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 4.37/4.54 inference(quant_intro,[status(thm)],[222])).
% 4.37/4.54 tff(224,plain,
% 4.37/4.54 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), rewrite(((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)) <=> (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))))),
% 4.37/4.54 inference(bind,[status(th)],[])).
% 4.37/4.54 tff(225,plain,
% 4.37/4.54 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 4.37/4.54 inference(quant_intro,[status(thm)],[224])).
% 4.37/4.54 tff(226,plain,
% 4.37/4.54 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 4.37/4.54 inference(rewrite,[status(thm)],[])).
% 4.37/4.54 tff(227,plain,
% 4.37/4.54 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 4.37/4.54 inference(bind,[status(th)],[])).
% 4.37/4.54 tff(228,plain,
% 4.37/4.54 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 4.37/4.54 inference(quant_intro,[status(thm)],[227])).
% 4.37/4.54 tff(229,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k22_filter_2')).
% 4.37/4.54 tff(230,plain,
% 4.37/4.54 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[229, 228])).
% 4.37/4.54 tff(231,plain,
% 4.37/4.54 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[230, 226])).
% 4.37/4.54 tff(232,plain,(
% 4.37/4.54 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 4.37/4.54 inference(skolemize,[status(sab)],[231])).
% 4.37/4.54 tff(233,plain,
% 4.37/4.54 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[232, 225])).
% 4.37/4.54 tff(234,plain,
% 4.37/4.54 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[233, 223])).
% 4.37/4.54 tff(235,plain,
% 4.37/4.54 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))))),
% 4.37/4.54 inference(rewrite,[status(thm)],[])).
% 4.37/4.54 tff(236,plain,
% 4.37/4.54 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))))),
% 4.37/4.54 inference(quant_inst,[status(thm)],[])).
% 4.37/4.54 tff(237,plain,
% 4.37/4.54 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0))))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[236, 235])).
% 4.37/4.54 tff(238,plain,
% 4.37/4.54 ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0))))),
% 4.37/4.54 inference(unit_resolution,[status(thm)],[237, 35, 34, 33, 41, 234])).
% 4.37/4.54 tff(239,plain,
% 4.37/4.54 (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))),
% 4.37/4.54 inference(unit_resolution,[status(thm)],[238, 221])).
% 4.37/4.54 tff(240,plain,
% 4.37/4.54 ((v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0))) | m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)),
% 4.37/4.54 inference(tautology,[status(thm)],[])).
% 4.37/4.54 tff(241,plain,
% 4.37/4.54 (m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)),
% 4.37/4.54 inference(unit_resolution,[status(thm)],[240, 239])).
% 4.37/4.54 tff(242,plain,
% 4.37/4.54 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)) | m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)) | m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 4.37/4.54 inference(rewrite,[status(thm)],[])).
% 4.37/4.54 tff(243,plain,
% 4.37/4.54 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)) | m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 4.37/4.54 inference(quant_inst,[status(thm)],[])).
% 4.37/4.54 tff(244,plain,
% 4.37/4.54 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)) | m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 4.37/4.54 inference(modus_ponens,[status(thm)],[243, 242])).
% 4.37/4.54 tff(245,plain,
% 4.37/4.54 (m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 4.37/4.54 inference(unit_resolution,[status(thm)],[244, 118, 241])).
% 4.37/4.54 tff(246,plain,
% 4.37/4.54 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))))),
% 4.37/4.54 inference(rewrite,[status(thm)],[])).
% 4.37/4.54 tff(247,plain,
% 4.37/4.54 (((~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))))))) <=> ((~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))))),
% 4.37/4.55 inference(rewrite,[status(thm)],[])).
% 4.37/4.55 tff(248,plain,
% 4.37/4.55 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))))))))),
% 4.37/4.55 inference(monotonicity,[status(thm)],[247])).
% 4.37/4.55 tff(249,plain,
% 4.37/4.55 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))))),
% 4.37/4.55 inference(transitivity,[status(thm)],[248, 246])).
% 4.37/4.55 tff(250,plain,
% 4.37/4.55 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))))))))),
% 4.37/4.55 inference(quant_inst,[status(thm)],[])).
% 4.37/4.55 tff(251,plain,
% 4.37/4.55 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))))))),
% 4.37/4.55 inference(modus_ponens,[status(thm)],[250, 249])).
% 4.37/4.55 tff(252,plain,
% 4.37/4.55 (~((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))),
% 4.37/4.55 inference(unit_resolution,[status(thm)],[251, 245, 201])).
% 4.37/4.55 tff(253,plain,
% 4.37/4.55 (((~((~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | ((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)))),
% 4.37/4.55 inference(tautology,[status(thm)],[])).
% 4.37/4.55 tff(254,plain,
% 4.37/4.55 ((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.55 inference(unit_resolution,[status(thm)],[253, 252])).
% 4.37/4.55 tff(255,plain,
% 4.37/4.55 (r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.55 inference(monotonicity,[status(thm)],[46])).
% 4.37/4.55 tff(256,plain,
% 4.37/4.55 (r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.55 inference(symmetry,[status(thm)],[255])).
% 4.37/4.55 tff(257,plain,
% 4.37/4.55 ((~r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))) <=> (~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)))),
% 4.37/4.55 inference(monotonicity,[status(thm)],[256])).
% 4.37/4.55 tff(258,plain,
% 4.37/4.55 (~r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.55 inference(or_elim,[status(thm)],[40])).
% 4.37/4.55 tff(259,plain,
% 4.37/4.55 (~r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.55 inference(modus_ponens,[status(thm)],[258, 257])).
% 4.37/4.55 tff(260,plain,
% 4.37/4.55 ((~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)))) | (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) | r1_filter_2(u1_struct_0(A!0), a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.55 inference(tautology,[status(thm)],[])).
% 4.37/4.55 tff(261,plain,
% 4.37/4.55 (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))),
% 4.37/4.55 inference(unit_resolution,[status(thm)],[260, 259, 254])).
% 4.37/4.55 tff(262,plain,
% 4.37/4.55 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))) | (~(r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))),
% 4.37/4.55 inference(tautology,[status(thm)],[])).
% 4.37/4.55 tff(263,plain,
% 4.37/4.55 (~(r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))),
% 4.37/4.55 inference(unit_resolution,[status(thm)],[262, 261])).
% 4.37/4.55 tff(264,plain,
% 4.37/4.55 ((r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))),
% 4.37/4.55 inference(tautology,[status(thm)],[])).
% 4.37/4.55 tff(265,plain,
% 4.37/4.55 ((~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))),
% 4.37/4.55 inference(unit_resolution,[status(thm)],[264, 263])).
% 4.37/4.55 tff(266,plain,
% 4.37/4.55 (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))),
% 4.37/4.55 inference(unit_resolution,[status(thm)],[265, 1])).
% 4.37/4.55 tff(267,plain,
% 4.37/4.55 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))))),
% 4.37/4.55 inference(bind,[status(th)],[])).
% 4.37/4.55 tff(268,plain,
% 4.37/4.55 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))),
% 4.37/4.55 inference(quant_intro,[status(thm)],[267])).
% 4.37/4.55 tff(269,plain,
% 4.37/4.55 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) <=> (~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))), ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (~(~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))))), rewrite((~(~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)))), ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))), trans(trans(monotonicity(rewrite((r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))) <=> (~((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))))), ((r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))) <=> (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (~((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))))))), rewrite((r2_hidden(A, a_2_0_filter_2(B, C)) <=> (~((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))))) <=> (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))), ((r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))) <=> (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))), rewrite((~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))) <=> (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))), ((r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))) <=> (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))) <=> ((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))))), rewrite(((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))))),
% 4.37/4.55 inference(bind,[status(th)],[])).
% 4.37/4.55 tff(270,plain,
% 4.37/4.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))),
% 4.37/4.55 inference(quant_intro,[status(thm)],[269])).
% 4.37/4.55 tff(271,plain,
% 4.37/4.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))),
% 4.37/4.55 inference(rewrite,[status(thm)],[])).
% 4.37/4.55 tff(272,plain,
% 4.37/4.55 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))), (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))), (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))))), rewrite((r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C))) <=> (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))))),
% 4.37/4.55 inference(bind,[status(th)],[])).
% 4.37/4.55 tff(273,plain,
% 4.37/4.55 (![A: $i, B: $i, C: $i] : (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))),
% 4.37/4.55 inference(quant_intro,[status(thm)],[272])).
% 4.37/4.55 tff(274,axiom,(![A: $i, B: $i, C: $i] : (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fraenkel_a_2_0_filter_2')).
% 4.37/4.55 tff(275,plain,
% 4.37/4.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))),
% 4.37/4.55 inference(modus_ponens,[status(thm)],[274, 273])).
% 4.37/4.55 tff(276,plain,
% 4.37/4.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))),
% 4.37/4.55 inference(modus_ponens,[status(thm)],[275, 271])).
% 4.37/4.55 tff(277,plain,(
% 4.37/4.55 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))),
% 4.37/4.55 inference(skolemize,[status(sab)],[276])).
% 4.37/4.55 tff(278,plain,
% 4.37/4.55 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))),
% 4.37/4.55 inference(modus_ponens,[status(thm)],[277, 270])).
% 4.37/4.55 tff(279,plain,
% 4.37/4.55 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))),
% 4.37/4.55 inference(modus_ponens,[status(thm)],[278, 268])).
% 4.37/4.55 tff(280,plain,
% 4.37/4.55 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))),
% 4.37/4.55 inference(rewrite,[status(thm)],[])).
% 4.37/4.55 tff(281,plain,
% 4.37/4.55 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))),
% 4.37/4.55 inference(rewrite,[status(thm)],[])).
% 4.37/4.55 tff(282,plain,
% 4.37/4.55 ((~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))) <=> (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))),
% 4.37/4.55 inference(rewrite,[status(thm)],[])).
% 4.37/4.55 tff(283,plain,
% 4.37/4.55 ((((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) <=> (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))),
% 4.37/4.55 inference(rewrite,[status(thm)],[])).
% 4.37/4.55 tff(284,plain,
% 4.37/4.55 ((~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))) <=> (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))),
% 4.37/4.56 inference(monotonicity,[status(thm)],[283])).
% 4.37/4.56 tff(285,plain,
% 4.37/4.56 ((~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))) <=> (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))),
% 4.37/4.56 inference(transitivity,[status(thm)],[284, 282])).
% 4.37/4.56 tff(286,plain,
% 4.37/4.56 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))),
% 4.37/4.56 inference(monotonicity,[status(thm)],[285])).
% 4.37/4.56 tff(287,plain,
% 4.37/4.56 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))),
% 4.37/4.56 inference(transitivity,[status(thm)],[286, 281])).
% 4.37/4.56 tff(288,plain,
% 4.37/4.56 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))))),
% 4.37/4.56 inference(monotonicity,[status(thm)],[287])).
% 4.37/4.56 tff(289,plain,
% 4.37/4.56 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))),
% 4.37/4.56 inference(transitivity,[status(thm)],[288, 280])).
% 4.37/4.56 tff(290,plain,
% 4.37/4.56 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))),
% 4.37/4.56 inference(quant_inst,[status(thm)],[])).
% 4.37/4.56 tff(291,plain,
% 4.37/4.56 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))),
% 4.37/4.56 inference(modus_ponens,[status(thm)],[290, 289])).
% 4.37/4.56 tff(292,plain,
% 4.37/4.56 (~(((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))),
% 4.37/4.56 inference(unit_resolution,[status(thm)],[291, 35, 34, 33, 41, 279])).
% 4.37/4.56 tff(293,plain,
% 4.37/4.56 ((((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))),
% 4.37/4.56 inference(tautology,[status(thm)],[])).
% 4.37/4.56 tff(294,plain,
% 4.37/4.56 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))),
% 4.37/4.56 inference(unit_resolution,[status(thm)],[293, 292])).
% 4.37/4.56 tff(295,plain,
% 4.37/4.56 ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))),
% 4.37/4.56 inference(unit_resolution,[status(thm)],[294, 266])).
% 4.37/4.56 tff(296,plain,
% 4.37/4.56 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))) | m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 4.37/4.56 inference(tautology,[status(thm)],[])).
% 4.37/4.56 tff(297,plain,
% 4.37/4.56 (m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 4.37/4.56 inference(unit_resolution,[status(thm)],[296, 261])).
% 4.37/4.56 tff(298,plain,
% 4.37/4.56 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))))),
% 4.37/4.56 inference(bind,[status(th)],[])).
% 4.37/4.56 tff(299,plain,
% 4.37/4.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 4.37/4.56 inference(quant_intro,[status(thm)],[298])).
% 4.37/4.56 tff(300,plain,
% 4.37/4.56 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))))),
% 4.37/4.56 inference(bind,[status(th)],[])).
% 4.37/4.56 tff(301,plain,
% 4.37/4.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 4.37/4.56 inference(quant_intro,[status(thm)],[300])).
% 4.37/4.56 tff(302,plain,
% 4.37/4.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 4.37/4.56 inference(transitivity,[status(thm)],[301, 299])).
% 4.37/4.56 tff(303,plain,
% 4.37/4.56 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))))),
% 4.37/4.56 inference(bind,[status(th)],[])).
% 4.37/4.56 tff(304,plain,
% 4.37/4.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 4.37/4.56 inference(quant_intro,[status(thm)],[303])).
% 4.37/4.56 tff(305,plain,
% 4.37/4.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 4.37/4.56 inference(rewrite,[status(thm)],[])).
% 4.37/4.56 tff(306,plain,
% 4.37/4.56 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite((r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))) <=> ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))), ((m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> (m1_subset_1(D, u1_struct_0(A)) => ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))), rewrite((m1_subset_1(D, u1_struct_0(A)) => ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))), ((m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))))),
% 4.37/4.56 inference(bind,[status(th)],[])).
% 4.37/4.56 tff(307,plain,
% 4.37/4.56 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 4.37/4.56 inference(quant_intro,[status(thm)],[306])).
% 4.37/4.56 tff(308,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t63_filter_2')).
% 4.37/4.56 tff(309,plain,
% 4.37/4.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 4.37/4.56 inference(modus_ponens,[status(thm)],[308, 307])).
% 4.37/4.56 tff(310,plain,
% 4.37/4.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 4.37/4.56 inference(modus_ponens,[status(thm)],[309, 305])).
% 4.37/4.56 tff(311,plain,(
% 4.37/4.56 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 4.37/4.56 inference(skolemize,[status(sab)],[310])).
% 4.37/4.56 tff(312,plain,
% 4.37/4.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 4.37/4.56 inference(modus_ponens,[status(thm)],[311, 304])).
% 4.37/4.56 tff(313,plain,
% 4.37/4.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 4.37/4.56 inference(modus_ponens,[status(thm)],[312, 302])).
% 4.37/4.56 tff(314,plain,
% 4.37/4.56 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C))))))))),
% 4.37/4.56 inference(rewrite,[status(thm)],[])).
% 4.37/4.56 tff(315,plain,
% 4.37/4.56 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C))))))))),
% 4.37/4.56 inference(quant_inst,[status(thm)],[])).
% 4.37/4.56 tff(316,plain,
% 4.37/4.56 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))),
% 4.37/4.56 inference(modus_ponens,[status(thm)],[315, 314])).
% 4.37/4.56 tff(317,plain,
% 4.37/4.56 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))),
% 4.37/4.56 inference(unit_resolution,[status(thm)],[316, 35, 34, 33, 313])).
% 4.37/4.56 tff(318,plain,
% 4.37/4.56 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (~(((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (~(((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)))))))),
% 4.37/4.56 inference(rewrite,[status(thm)],[])).
% 4.37/4.56 tff(319,plain,
% 4.37/4.56 (((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, k5_lattices(A!0), C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, k5_lattices(A!0), D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C))))))) <=> ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (~(((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)))))))),
% 4.37/4.56 inference(rewrite,[status(thm)],[])).
% 4.37/4.56 tff(320,plain,
% 4.37/4.56 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, k5_lattices(A!0), C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, k5_lattices(A!0), D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (~(((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C))))))))),
% 4.37/4.57 inference(monotonicity,[status(thm)],[319])).
% 4.37/4.57 tff(321,plain,
% 4.37/4.57 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, k5_lattices(A!0), C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, k5_lattices(A!0), D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (~(((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)))))))),
% 4.37/4.57 inference(transitivity,[status(thm)],[320, 318])).
% 4.37/4.57 tff(322,plain,
% 4.37/4.57 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, k5_lattices(A!0), C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, k5_lattices(A!0), D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)))))))),
% 4.37/4.57 inference(quant_inst,[status(thm)],[])).
% 4.37/4.57 tff(323,plain,
% 4.37/4.57 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (~(((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C))))))),
% 4.37/4.57 inference(modus_ponens,[status(thm)],[322, 321])).
% 4.37/4.57 tff(324,plain,
% 4.37/4.57 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (~(((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C))))))),
% 4.37/4.57 inference(unit_resolution,[status(thm)],[323, 317, 221])).
% 4.37/4.57 tff(325,plain,
% 4.37/4.57 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (~(((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (~(((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1))))))),
% 4.37/4.57 inference(rewrite,[status(thm)],[])).
% 4.37/4.57 tff(326,plain,
% 4.37/4.57 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (~(((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1))))))),
% 4.37/4.57 inference(quant_inst,[status(thm)],[])).
% 4.37/4.57 tff(327,plain,
% 4.37/4.57 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (~(((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))),
% 4.37/4.57 inference(modus_ponens,[status(thm)],[326, 325])).
% 4.37/4.57 tff(328,plain,
% 4.37/4.57 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))),
% 4.37/4.57 inference(unit_resolution,[status(thm)],[327, 41, 324])).
% 4.37/4.57 tff(329,plain,
% 4.37/4.57 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))))),
% 4.37/4.57 inference(bind,[status(th)],[])).
% 4.37/4.57 tff(330,plain,
% 4.37/4.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 4.37/4.57 inference(quant_intro,[status(thm)],[329])).
% 4.37/4.57 tff(331,plain,
% 4.37/4.57 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))))),
% 4.37/4.57 inference(bind,[status(th)],[])).
% 4.37/4.57 tff(332,plain,
% 4.37/4.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 4.37/4.57 inference(quant_intro,[status(thm)],[331])).
% 4.37/4.57 tff(333,plain,
% 4.37/4.57 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))))),
% 4.37/4.57 inference(bind,[status(th)],[])).
% 4.37/4.57 tff(334,plain,
% 4.37/4.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 4.37/4.57 inference(quant_intro,[status(thm)],[333])).
% 4.37/4.57 tff(335,plain,
% 4.37/4.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 4.37/4.57 inference(transitivity,[status(thm)],[334, 332])).
% 4.37/4.57 tff(336,plain,
% 4.37/4.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))))),
% 4.37/4.57 inference(bind,[status(th)],[])).
% 4.37/4.57 tff(337,plain,
% 4.37/4.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 4.37/4.57 inference(quant_intro,[status(thm)],[336])).
% 4.37/4.57 tff(338,plain,
% 4.37/4.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 4.37/4.57 inference(rewrite,[status(thm)],[])).
% 4.37/4.57 tff(339,plain,
% 4.37/4.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))))),
% 4.37/4.57 inference(bind,[status(th)],[])).
% 4.37/4.57 tff(340,plain,
% 4.37/4.57 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 4.37/4.57 inference(quant_intro,[status(thm)],[339])).
% 4.37/4.57 tff(341,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t41_lattices')).
% 4.37/4.57 tff(342,plain,
% 4.37/4.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 4.37/4.57 inference(modus_ponens,[status(thm)],[341, 340])).
% 4.37/4.57 tff(343,plain,
% 4.37/4.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 4.37/4.57 inference(modus_ponens,[status(thm)],[342, 338])).
% 4.37/4.57 tff(344,plain,(
% 4.37/4.57 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 4.37/4.57 inference(skolemize,[status(sab)],[343])).
% 4.37/4.57 tff(345,plain,
% 4.37/4.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 4.37/4.57 inference(modus_ponens,[status(thm)],[344, 337])).
% 4.37/4.57 tff(346,plain,
% 4.37/4.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 4.37/4.57 inference(modus_ponens,[status(thm)],[345, 335])).
% 4.37/4.57 tff(347,plain,
% 4.37/4.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 4.37/4.57 inference(modus_ponens,[status(thm)],[346, 330])).
% 4.37/4.57 tff(348,plain,
% 4.37/4.57 (v13_lattices(A!0)),
% 4.37/4.57 inference(or_elim,[status(thm)],[40])).
% 4.37/4.57 tff(349,plain,
% 4.37/4.57 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B)))),
% 4.37/4.57 inference(rewrite,[status(thm)],[])).
% 4.37/4.57 tff(350,plain,
% 4.37/4.57 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B)))),
% 4.37/4.57 inference(quant_inst,[status(thm)],[])).
% 4.37/4.57 tff(351,plain,
% 4.37/4.57 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))),
% 4.37/4.57 inference(modus_ponens,[status(thm)],[350, 349])).
% 4.37/4.57 tff(352,plain,
% 4.37/4.57 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))),
% 4.37/4.57 inference(unit_resolution,[status(thm)],[351, 35, 34, 33, 348, 347])).
% 4.37/4.57 tff(353,plain,
% 4.37/4.57 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.57 inference(rewrite,[status(thm)],[])).
% 4.37/4.57 tff(354,plain,
% 4.37/4.57 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.57 inference(quant_inst,[status(thm)],[])).
% 4.37/4.57 tff(355,plain,
% 4.37/4.57 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B!1)),
% 4.37/4.57 inference(modus_ponens,[status(thm)],[354, 353])).
% 4.37/4.57 tff(356,plain,
% 4.37/4.57 (r3_lattices(A!0, k5_lattices(A!0), B!1)),
% 4.37/4.57 inference(unit_resolution,[status(thm)],[355, 41, 352])).
% 4.37/4.57 tff(357,plain,
% 4.37/4.57 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | ((~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))),
% 4.37/4.57 inference(rewrite,[status(thm)],[])).
% 4.37/4.57 tff(358,plain,
% 4.37/4.57 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) <=> ((~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))),
% 4.37/4.57 inference(rewrite,[status(thm)],[])).
% 4.37/4.57 tff(359,plain,
% 4.37/4.57 ((~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))) <=> (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))),
% 4.37/4.57 inference(rewrite,[status(thm)],[])).
% 4.37/4.57 tff(360,plain,
% 4.37/4.57 ((((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0))))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))) <=> (((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))),
% 4.37/4.57 inference(rewrite,[status(thm)],[])).
% 4.37/4.57 tff(361,plain,
% 4.37/4.57 ((~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0))))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))) <=> (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))),
% 4.37/4.57 inference(monotonicity,[status(thm)],[360])).
% 4.37/4.57 tff(362,plain,
% 4.37/4.57 ((~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0))))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))) <=> (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))),
% 4.37/4.57 inference(transitivity,[status(thm)],[361, 359])).
% 4.37/4.57 tff(363,plain,
% 4.37/4.57 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0))))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) <=> ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))),
% 4.37/4.57 inference(monotonicity,[status(thm)],[362])).
% 4.37/4.57 tff(364,plain,
% 4.37/4.57 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0))))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))) <=> ((~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))),
% 4.37/4.57 inference(transitivity,[status(thm)],[363, 358])).
% 4.37/4.57 tff(365,plain,
% 4.37/4.57 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0))))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | ((~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))))),
% 4.37/4.57 inference(monotonicity,[status(thm)],[364])).
% 4.37/4.57 tff(366,plain,
% 4.37/4.57 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0))))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))),
% 4.37/4.57 inference(transitivity,[status(thm)],[365, 357])).
% 4.37/4.57 tff(367,plain,
% 4.37/4.57 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0))))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))))),
% 4.37/4.58 inference(quant_inst,[status(thm)],[])).
% 4.37/4.58 tff(368,plain,
% 4.37/4.58 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~(((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))) <=> r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)))))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))))),
% 4.37/4.58 inference(modus_ponens,[status(thm)],[367, 366])).
% 4.37/4.58 tff(369,plain,
% 4.37/4.58 (~(((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[368, 356, 328, 297])).
% 4.37/4.58 tff(370,plain,
% 4.37/4.58 ((((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))),
% 4.37/4.58 inference(tautology,[status(thm)],[])).
% 4.37/4.58 tff(371,plain,
% 4.37/4.58 ((~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)))),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[370, 369])).
% 4.37/4.58 tff(372,plain,
% 4.37/4.58 (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)))),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[371, 1])).
% 4.37/4.58 tff(373,plain,
% 4.37/4.58 (((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) | r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)),
% 4.37/4.58 inference(tautology,[status(thm)],[])).
% 4.37/4.58 tff(374,plain,
% 4.37/4.58 (r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[373, 372])).
% 4.37/4.58 tff(375,plain,
% 4.37/4.58 ((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))),
% 4.37/4.58 inference(tautology,[status(thm)],[])).
% 4.37/4.58 tff(376,plain,
% 4.37/4.58 ((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[375, 297])).
% 4.37/4.58 tff(377,plain,
% 4.37/4.58 ($false),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[376, 374, 295])).
% 4.37/4.58 tff(378,plain,(~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))), inference(lemma,lemma(discharge,[]))).
% 4.37/4.58 tff(379,plain,
% 4.37/4.58 ((r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.58 inference(tautology,[status(thm)],[])).
% 4.37/4.58 tff(380,plain,
% 4.37/4.58 (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[379, 263])).
% 4.37/4.58 tff(381,plain,
% 4.37/4.58 (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[380, 378])).
% 4.37/4.58 tff(382,plain,
% 4.37/4.58 ((((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))),
% 4.37/4.58 inference(tautology,[status(thm)],[])).
% 4.37/4.58 tff(383,plain,
% 4.37/4.58 ((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[382, 292])).
% 4.37/4.58 tff(384,plain,
% 4.37/4.58 (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)))),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[383, 381])).
% 4.37/4.58 tff(385,plain,
% 4.37/4.58 ((((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | ((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.58 inference(tautology,[status(thm)],[])).
% 4.37/4.58 tff(386,plain,
% 4.37/4.58 (((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[385, 369])).
% 4.37/4.58 tff(387,plain,
% 4.37/4.58 ((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))),
% 4.37/4.58 inference(unit_resolution,[status(thm)],[386, 378])).
% 4.37/4.58 tff(388,plain,
% 4.37/4.58 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0))))),
% 4.37/4.58 inference(rewrite,[status(thm)],[])).
% 4.37/4.58 tff(389,plain,
% 4.37/4.58 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0))))),
% 4.37/4.58 inference(quant_inst,[status(thm)],[])).
% 4.37/4.58 tff(390,plain,
% 4.37/4.58 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))),
% 4.37/4.58 inference(modus_ponens,[status(thm)],[389, 388])).
% 4.37/4.58 tff(391,plain,
% 4.37/4.58 (r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))),
% 4.37/4.60 inference(unit_resolution,[status(thm)],[390, 352, 297])).
% 4.37/4.60 tff(392,plain,
% 4.37/4.60 ((~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)))) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))),
% 4.37/4.60 inference(tautology,[status(thm)],[])).
% 4.37/4.60 tff(393,plain,
% 4.37/4.60 ((~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))),
% 4.37/4.60 inference(unit_resolution,[status(thm)],[392, 391])).
% 4.37/4.60 tff(394,plain,
% 4.37/4.60 (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)),
% 4.37/4.60 inference(unit_resolution,[status(thm)],[393, 387])).
% 4.37/4.60 tff(395,plain,
% 4.37/4.60 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1))) | r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1), u1_struct_0(A!0)), B!1)),
% 4.37/4.60 inference(tautology,[status(thm)],[])).
% 4.37/4.60 tff(396,plain,
% 4.37/4.60 ($false),
% 4.37/4.60 inference(unit_resolution,[status(thm)],[395, 394, 384])).
% 4.37/4.60 % SZS output end Proof
% 4.37/4.60 % E exiting
%------------------------------------------------------------------------------